The elves (here: Sithi) in Tad William's Memory, Sorrow and Thorn series are technically immortal in the sense of "living for a veeeeeeery long time", but they do grow old and weaker, and they can be killed. One of the main villains is so ancient that everyone comments on how unusual that is. There's a lot of magic involved, and she also chose to fall into a deep slumber for several decades (for preservation?). Also, they have a very low birthrate.

I found this approach pretty good, actually.